Determining the empirical formula from experimental data involves converting mass percentages or masses of elements to moles, finding the simplest whole-number mole ratio, and using that ratio as subscripts in the empirical formula.
Steps to Determine Empirical Formula
Here's a detailed breakdown of the process:
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Obtain the Mass Data: This is usually provided as either:
- Percent composition: The percentage by mass of each element in the compound.
- Actual masses: The mass of each element in a given mass of the compound.
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Convert Mass to Moles: If you have percent composition, assume you have 100 g of the compound. This makes the percentages directly equivalent to grams. Then, for each element, convert grams to moles using the element's molar mass (from the periodic table). The formula for this conversion is:
Moles = (Mass in grams) / (Molar mass)
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Determine the Mole Ratio: Divide the number of moles of each element by the smallest number of moles calculated in the previous step. This gives you a preliminary mole ratio.
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Convert to Whole Numbers: The mole ratios obtained in the previous step may not be whole numbers. To obtain whole-number subscripts for the empirical formula:
- If the ratios are close to whole numbers (e.g., 1.1, 2.9), round them to the nearest whole number.
- If the ratios are not close to whole numbers (e.g., 1.5, 2.33, 1.25), multiply all the ratios by the smallest integer that will convert them all to whole numbers. Common multipliers are 2 (for .5), 3 (for .33 or .67), and 4 (for .25 or .75).
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Write the Empirical Formula: Use the whole-number mole ratios obtained in the previous step as subscripts for the corresponding elements in the empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in the compound.
Example
Let's say a compound is found to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen.
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Mass Data:
- C: 40.0 g
- H: 6.7 g
- O: 53.3 g
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Convert to Moles:
- C: (40.0 g) / (12.01 g/mol) = 3.33 mol
- H: (6.7 g) / (1.01 g/mol) = 6.63 mol
- O: (53.3 g) / (16.00 g/mol) = 3.33 mol
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Determine the Mole Ratio: Divide each by the smallest number of moles (3.33 mol).
- C: (3.33 mol) / (3.33 mol) = 1
- H: (6.63 mol) / (3.33 mol) = 1.99 ≈ 2
- O: (3.33 mol) / (3.33 mol) = 1
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Convert to Whole Numbers: The ratios are already close to whole numbers.
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Write the Empirical Formula: The empirical formula is CH2O.
Tips and Considerations
- Precision: The accuracy of the empirical formula depends on the precision of the experimental data.
- Molecular Formula: The empirical formula is the simplest whole-number ratio. To determine the molecular formula, you need the molar mass of the compound. The molecular formula is a whole-number multiple of the empirical formula.
- Hydrates: For hydrated compounds, the water molecules must also be accounted for in the empirical formula. The process is similar, involving converting the mass of water to moles and finding the mole ratio.